We study the convergence to equilibrium of the mean field PDE associated with the derivative-free methodologies for solving inverse problems that are presented by Garbuno-Inigo etal (2020 SIAM J. Appl. Dyn. Syst. 19 412–41), Herty and Visconti (2018 arXiv:1811.09387). We show stability estimates in the Euclidean Wasserstein distance for the mean field PDE by using optimal transport arguments. As a consequence, this recovers the convergence towards equilibrium estimates by Garbuno-Inigo etal (2020 SIAM J. Appl. Dyn. Syst. 19 412–41) in the case of a linear forward model.

我们研究了与 Garbuno-Inigo等人(2020 SIAM J. Appl. Dyn. Syst. 19 412–41)、Herty 和 Visconti提出的用于求解逆问题的无导数方法相关的平均场 PDE 的平衡收敛（2018 年 arXiv：1811.09387）。我们通过使用最佳传输参数显示了平均场 PDE 的欧几里得 Wasserstein 距离的稳定性估计。因此，在线性前向模型的情况下，这恢复了 Garbuno-Inigo等人(2020 SIAM J. Appl. Dyn. Syst. 19 412-41)对均衡估计的收敛。